Hi Scott,
I'm sorry you've been experiencing problems with the app.
If you have valid use cases where products do not have barcodes, all you need to do is go to the app's settings page, and choose "Disable product identifiers." As the text reads, the app will continue to send identifiers when present, but will send products without barcodes with a special flag telling google it's not supposed to have a barcode.
Another strategy, as Joel suggested, would be to add a tag to products you do not wish to publish at this time, and choose that collection for publishing in the settings.
I can't speak to what other apps may have done with shop metafields. However, Google Shopping only installs/uses MPN, Age Group, Gender, and Google Product Type metafields - the rest of the product data is taken from Product/Variant fields and options.
Cheers,
Shawn